On Existence of Static Metric Extensions in General Relativity
نویسنده
چکیده
Abstract: Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik [4]. We show that, for any metric on B̄1 that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists an asymptotically flat and scalar flat static metric extension in M = R \B1 such that it satisfies Bartnik’s geometric boundary condition [4] on ∂B1.
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